Modeling In-Use Engine Conditions and the Resulting Emissions
by
Todd Haugsjaa
B.S.. Mechanical Engineering
University of Massachusetts at Amherst, 1997
Submitted to the Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
February 1999
© 1999 Massachusetts Institute of Technology
All rights reserved
/
/
/7i
Signature of Author
Department
e anical Engineering
January 15. 1999
a
Certified by
Wai K. Cheng
Professor of Mechanical Engineering
Supervisor
Accepted by
Ain A. Sonin
Chairman, Department Committee on Graduate Studies
I
Modeling In-Use Engine Conditions and the Resulting Emissions
by
Todd Haugsjaa
Submitted to the Department of Mechanical Engineering
on December 28. 1998 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Mechanical Engineering
ABSTRACT
A model for evaluating the engine-out emission levels under different driving situations
has been developed. By adopting different driving characteristics (hard accelerations.
timid driving, cruise-control speeds. or erratic driving) and by assigning different driving
routes, the mode: produces second-by-second emission levels from the car. In this thesis.
quasi-static emission maps were used for emission calculation. As such, a strong
correlation between emission mass flowrates and brake power has been established
except when enrichment is encountered. At low powers, where stoichiometric mixtures
are seen, a linear brake power dependence is obtained for HC, CO, and NO emissions. At
points where a high level of enrichment occurs, HC emissions increase, much higher CO
emissions are seen and NO emissions decrease considerably.
Thesis Supervisor: Wai K. Cheng
Title: Professor of Mechanical Engineering
2
Contents
Abstract
2
Chapter 1 - Introduction
4
1.1 Background
4
1.2 Objective
7
Chapter 2 - Engine Quasi-Static Emissions Data
9
Chapter 3 - Computer Model
14
3.1 Overview
14
3.2 Description of Procedure
15
29
Chapter 4 - Results and Discussion
4.1 Following the Velocity Profile in the Federal Test Procedure (FTP)
29
4.2 Following the Road Profile
37
4.3 Conclusions
45
47
Appendix
A: Ford Contour Specifications
47
B: Data File Formats
48
C: FORTRAN Code
52
78
References
3
Chapter 1 - Introduction
1.1 Background
Recently, out of concern for their environmental impact, more and more attention
has been paid to the emission levels exiting the engine and tailpipe of vehicles. In an
effort to reduce these levels, much research has been done to model emission formation
mechanisms inside an engine. See [1] for an account of the in-cylinder hydrocarbon
formation mechanisms. As helpful as these models are in understanding basic
mechanisms, laboratory studies seldom encompass what engines are subjected to under
real world driving conditions; in particular, the effects of transient loads and speeds, open
loop enrichment, and other unsteady events need to be addressed.
Understanding the relationship between transient engine conditions and emissions
is essential. Such an understanding will highlight important unsteady engine emission
mechanisms and will assist the engineering efforts to lower their levels. It will also
provide a basis for assessing the impact that vehicle emissions will have on regional air
quality.
There are several methods of obtaining vehicle emission data for analysis. The
data may be collected via:
1) quasi-static operation where engine conditions are held constant with a dynamometer
for each data point. From this data, a quasi-static emission map can be constructed.
The map is typically represented by contours of an exhaust species' specific emission
against engine variables such as torque and speed.
2) dynamic drive-cycles, where either:
4
a) a representative driving cycle is followed with the vehicle on a chassis
dynamometer which imposes an appropriate load/speed relationship, or
b) an on-the-road test is conducted, where the vehicle is equipped with apparatus to
measure emissions on-board.
1.1.1 Quasi-static Maps
Quasi-static mapping is readily available as a standard engine database and
provides the basic emission characteristics for a vehicle. The map is vehicle specific
because the emission levels are dependent on the engine controller setting for levels of
EGR, spark timing and fuel metering. The emission levels of the vehicle can be mapped
against load and speed under the particular engine management system.
While quasi-static maps are common, they do not reflect the transients that occur
while driving (open-loop enrichment, prior engine operating trajectory effects, catalyst
lags, etc.). To get closer to real-world emission evaluations, dynamic testing methods
have been developed to analyze emission levels in a driving simulation.
1.1.2 Drive-cycles Conducted on a Dynamometer
The drive-cycle tests are more realistic than quasi-static maps since the engine
operating conditions are continuously changing during the data collection process. The
test produces second by second emissions data while the vehicle follows a predetermined
velocity profile. The standard driving cycle used is the Federal Testing Procedure (FTP).
While it provides a common ground for vehicle certifications, the procedure differs
substantially from real-world driving. In particular, it ignores the effect of road grades
5
and hard accelerations and thus a substantial part of the driving experience. This
shortcoming is illustrated in Figure 1.1 where a Ford Taurus on a flat road was driven to
its maximum accelerating and decelerating limits from steady speeds of 0, 10, 20, etc.
mph [2]. Plotted with a solid line against the vehicle's speed are the achievable
accelerations and decelerations of the car; thus these lines represent the operating
speed/acceleration envelope. On the same plot, the dots inside this envelope indicate the
accelerations and decelerations that occur during the FTP cycle for each second.
'0-
S
LO
I
-5
Z
tU
-15
-20
0
10
20
30
40
50
60
70
80
90
Velocity (MPH)
Figure 1.1: The extreme accelerations of a 1991 Ford Taurus with a 3.OL V-6 engine
plotted against vehicle speed (solid line) and the accelerations reached during the FTP
cycle (dots).
While the boundary of the operating envelope represents extreme driving
conditions, Figure 1.1 illustrates that much of the achievable vehicle operating modes are
not addressed by the FTP. Furthermore, the data from the FTP are aggregated into three
6
phases. Thus, while suitable for comparing vehicles, it cannot easily be used to make a
realistic emission assessment.
1.1.3 On-board Emissions Measurements
Since on-the-road driving conditions can differ substantially from the FTP
conditions, use of the latter data could seriously under-assess real-world vehicle
emissions. It has become evident that there are crucial vehicle operating conditions
where emission levels can far exceed those under normal driving. To identify these
conditions, it is necessary to evaluate real-world driving emissions by means of on-board
emissions measurements.
\ On-board equipment allows the analysis of many different conditions encountered
on the road such as hard acceleration up hills, steady or erratic driving characteristics,
AC loading, etc. The down side to this is the major time and money required for
outfitting a vehicle with the proper equipment and computers and then processing all the
data into a comprehensive form.
1.2 Objective
Realizing the importance of understanding real-world driving emission levels and
considering the large resources required to examine them in practice, it is attractive to
develop a phenomenological model that can simulate a driving route and produce
expected emission levels. The overall strategy is to have a vehicle driving model that
relates the vehicle on-the-road behavior to engine operating conditions, and then relate
the latter to emissions. The model is phenomenological in the sense that it is used as a
7
structure to summarize data from an on-the-road test with different vehicles and with
different route characteristics. This investigation is the first phase in an effort to model
real world driving emissions. The scope is to make use of the basic information from
quasi-static maps in reproducing the engine out emissions for a given road and driving
profile.
The output of this phase 1 effort provides the basis for comparison with the data
obtained from on-board emissions equipment in a road test with the same road and
driving profile for phase 2. By comparing these results, the departure from quasi-static
behavior can be quantified and appropriate transient models can be developed.
In this phase of the study only the engine out data are considered. The tailpipe
emissions are very much catalyst specific, and the catalyst is responsible for much of the
transient tailpipe emissions behavior. The study of these effects is postponed to phase 2
of the project.
8
Chapter 2 - Engine Quasi-Static Emissions Data
For the first stage of the project, a basic quasi-static map was needed to evaluate
the model. A dynamometer mounted 2.0 liter Ztec engine from a Ford Contour was used
to map the quasi-static engine out emission levels and the specific fuel consumption (sfc).
Torque values range from 40 to 140 N-m; the engine speed ranges from 1500 to 4000
rpm. The engine was managed by the Ford EEC IV controller unit under all time.
When mapped against torque and engine speed, certain trends in the emission
indexes (EI) and specific emissions for individual species can be seen. The El value of an
emission species is defined by the mass emission normalized by the fuel mass input to the
engine. This gives a good indication of how much of the fuel becomes a particular
emission species. The specific emission is the mass flowrate of the emission normalized
by the brake power. This takes into account fuel efficiency of the engine (sfc) by
comparing the emission species to the brake power produced. For example, two vehicles
may have the same emission index maps, but if one has higher values of sfc (it is less fuel
efficient), it will have higher emission flowrates than the other car.
The sfc predominantly decreases with increasing torque due to lower throttling
losses, and at high torque sfc decreases as speed increases (Figure 2.1 a). Values range
from 240 to 360 g/kW-hr. As torque and speed increase, the air to fuel equivalence ratio
(Lambda) decreases according to the engine management strategy (Figure 2. 1b). The CO
emission index (EICO) and specific CO emission (sCO) (Figures 2. lc-d) both increase
accordingly. The phenomenon responsible here is the tendency of the enriched mixtures
to burn incompletely. Thus, high CO emissions occur when lambda is below 1 (the
mixture is fuel rich) as is demonstrated in Figure 2.2. From this, it can be seen that EICO
9
is only a function of lambda, regardless of the speed and torque. Ranges seen are from
0.84 to 1 for lambda, 1%to 60% for EICO, and 20 to 140 g/kW-hr for sCO. Inside the
boundary of -100 N-m and -3000 rpm, sCO stays at a relatively flat level of -20 g/kWhr. Beyond this boundary, the values increase rapidly with both speed and load to -140
g/kW-hr. Since the operating points in the FTP stay within the mentioned boundary,
radically high values of CO emissions are usually not seen in that test. Road driving,
however, often reaches beyond these boundaries and, as will be seen later in this thesis, it
results in heavy CO emissions.
lambda
Specific Fuel Consumption, sfc (g/kW-hr)
10140
84
+2
130
130
120
120
0.96.
110r......
90
60
80-
---
70.92
280
70
--
---
-
50.
60
00
50
20
~~
....
..
34'0
50 .......
0
40
40
1500
.......98
. ...........-
100
-
80
60
10
+24(
- 100
90
20
2
110 -
3000
2500
2000
2000
1500
4000
3500
.
0....
98
rpm
b
a
sCO (g/kW-hr)
EICO (g/100g fuel)
140
-----
+ 0110'
+--0
E100
100
z
20
90
90-
80
80
70-
70-
60-
60-
50
50
2
+ 20
40-
40
1500
0 120
100
120.
0
--
00140
50
.8
110
14
130
60
N
130
120
4000
3500
3000
2500
rpm
z
086
--
2000
3000
2500
3500
1500
4000
2000
3000
2500
3500
4000
rpm
rpm
d
c
Figure 2.1: Contour maps of (a) specific fuel consumption (sfc), (b) lambda, (c) Emission
Index CO levels (EICO), and (d) specific CO levels (sCO) all mapped against engine
torque and speed.
10
CO Emissions
-E 80 0 70
+
0
x~5
04
40
U)
r0
+
30
.M 20
E
W 10
C.)0
0.8
0.85
1
0.95
0.9
1.05
Lambda
Figure 2.2: Linear relationship between EICO and lambda.
The contour of EIHC (Figure 2.3a) has a valley in the middle ranges of torque
(100 N-m) and speed (3000 rpm), but has a small spread of only 1% to 1.3% over the
entire map. The sHC levels (Figure 2.3b) have a limited range of 2.5 to 4 g/kW-hr; since
sHC is the product of the EIHC and sfc, and the former values are relatively flat over the
map, the sHC values (Figure 2.3b) predominantly follow the trends of the sfc (Figure
2.1 a).
11
ElHC (g/1OOg
fuel)
~80-
sHC (g/kW-hr)
/
15
80
70
70
60
60
1 .2
..........
501
40
1500
3 5.................
50
2000
#-40
2500
3000
3500
4000
1500
rpm
2000
2500
3000
3500
4000
rpm
a
b
Figure 2.3: Contour maps of (a) Emission Index HC levels (EIHC), and (b) specific HC
levels (sHC) both mapped against engine torque and speed.
The values of EINO (Figure 2.4a) have a substantial spread of 1%to 6% over the
map. The values peak at around 3000 rpm and 100 N-m. Production of NO is both
sensitive to temperature and to the availability of oxygen. From the peak value at -3000
rpm and -100 N-m, the drop off of the EINO at higher torque and speed is due to
enrichment (see Figure 2. 1b); both the combustion temperature and the oxygen
availability are reduced with enrichment. Also at high speeds, the combustion phasing is
effectively retarded, leading to a lower combustion temperature. The drop off at low load
and rpm is due to a higher heat loss relative to the charge energy, again resulting in lower
combustion temperatures. Levels of sNO (Figure 2.4b) extend between 2 and 16 g/kWhr, with the high values encountered at low torque, high speed levels (due to high sfc
values at low torque).
12
EINO (g/1OOg
fuel)
sNO (g/kW-hr)
-0100
100
90
4
-904
80-
80-
70 -
70-
60
60
50 _
50
401500
40
2000
3000
2500
3500
4000
1500
12
8
2000
2500
3000
3500
4000
rpm
rpm
b
a
Figure 2.4: Contour maps of (a) Emission Index NO levels (EINO), and (b) specific NO
levels (sNO) both mapped against engine torque and speed.
While these maps give a good indication of how emissions relate to the engine
conditions, transient effects play a large role in determining the actual emissions. After
setting the groundwork for the model in this stage, stage 2 will identify how these
transients affect the emissions.
13
Chapter 3 - Computer Model
3.1 Overview
The model described in this thesis provides the second-by-second quasi-static
engine out emissions for a vehicle. It can either create a velocity profile for a vehicle
from a specified road profile or can follow a specified velocity profile (such as the FTP).
Of primary interest is the case for a given road profile since it represents real-world
driving scenarios. The case for a given velocity profile is also incorporated since it helps
in evaluating the emission modeling by computing the emission levels for a standardized
test profile that is available for every passenger car.
When following a road profile, the model uses topology data, stopping points and
speed limits for the route along with a pre-defined acceleration profile to create a time
profile of vehicle conditions. Conditions such as speed, acceleration and the
corresponding rpm and brake power are calculated and used to evaluate the emissions.
If a velocity profile is given as the input, the engine conditions are calculated
according to the road load requirements. For the FTP test, the road is assumed to be
level, so aerodynamic and road drag and acceleration are the only indicators of the power
requirements.
In both cases, once the engine operating conditions are found, the emissions are
then interpolated from quasi-static emissions maps for the engine. In this stage of
research, the emissions are determined solely from the quasi-static map. For future work,
the output from this will be compared to actual on-road tests. The vehicle used for this
stage is a Ford Contour with a 2.0 liter Ztec engine; specifications for the vehicle used in
this model are provided in Appendix A.
14
3.2 Description of Procedure
3.2.1 Using a Prescribed Road Profile
The procedure used to create the time profile of vehicle conditions from a road
elevation profile will be described first. The procedure of following a predetermined
velocity profile against time is a subset of the above and is discussed at the end.
The structure of the discussion below follows the sequence of information flow in
the computer program. The procedure of obtaining the various data is discussed.
3.2.1.1 Input Files
The program begins by reading in data files containing the road profile (distance
traveled, elevation, stop points, speed limits), physical car data (drag coefficients, frontal
area, wheel diameter, displacement, number of gears, min/max torque and rpm, overall
gear ratios), the shifting schedule (the engine speed at which upshifts and downshifts are
requested for different torques). Also read are the quasi-static engine maps for engine out
emission-indexes as well as the specific fuel consumption. The format of these files are
explained in Appendix B.
3.2.1.2 Creating the Road Profile
For a given route, the road profile was generated with a topographical route
selection program (TOPO!). By specifying a desired route on an electronic map, the
program will create a profile of elevation against distance traveled (not horizontal
distance). The image of this profile is saved as a compressed bitmap and is imported into
15
an image analysis program, ImagePro Plus. A tracer follows the elevation of the route.
The pixel coordinates of this trace (the origin being at the top-left corner of the image) are
recorded by the tracer and are saved to a file. The scale of the x- and y-axes must also be
noted in the number of pixels per the length in miles or feet.
A subroutine contained in the model converts the pixel information into miles
traveled and elevations in feet. It also reads a file containing the points along the route
where the speed limit changes and where stops occur. This data is combined with the
topological data and saved in another file for use by the main model. Once this is done,
the new file can be used for later runs of the program without converting the pixel
information again.
, An example of this procedure is the route from Central Square in Cambridge, MA
to the Route 128 interchange on Route 2. The route is marked on the TOPO! map in
Figure 3.1, and this route's elevation profile, produced by TOPO!, is in Figure 3.2. This
is a typical route taken by many commuters each day from the city to a suburban town
community.
16
Figure 3.1: TOPO! map of Cambridge, MA area with the route from Central Square
marked by a heavy line.
17
rnmtea inm I UFU! t9
I S Widllower Productions (www.topo.com)
Figure 3.2: TOPO! elevation profile of the route from Central Square in Cambridge, MA
to the Route 128 interchange on Route 2. The x-axis is the distance traveled (not
horizontal distance) in miles; the y-axis is the elevation in feet.
3.2.1.3 Shifting Schedule
The engine is connected to the wheels via the transmission. For a manual
transmission, the shifting schedule is driver specific; for an automatic transmission, it
depends on the shifting controller (either electronic or mechanical analog type) strategy.
In order to make this model less vehicle and driver specific and more applicable to any
vehicle, the shifting schedule was chosen to be a reasonable approximation of how most
automatic transmissions will shift. The procedure is based on a normalized engine speed
versus torque map on which the shifting boundaries are drawn; see Figure 3.3. An
upshift occurs when the operating conditions are above the upshift boundary (in region
A) and downshifts occur when they are below the downshift boundary (in region C).
18
Shifting Schedule
1.000
0.900
x
0.800
E
C.
0.700
E
0.600
Upshif t Boundary
0500
- - - - Dow nshift Boundary
A
z,.
0.400
a)
C/)
a)
0.300
B-
0.200
-
0.00-
-0.2
C
0
0.2
0.4
0.6
0.8
1
Torque Ratio, T/Tmax
Figure 3.3: Shifting Schedule. Upshifts are requested above the upshift boundary (in
region A) and downshifts are requested below the downshift boundary (in region C).
Points x, y, and z demonstrate a possible engine trajectory, where a hill is encountered.
For example (see trajectory xyz in the figure for the following discussion), say initially
the vehicle is traveling on a level road at a constant speed in fourth gear. Operating point
x in the stable region B on the map (no shifting required) represents this. Then a steep
hill is encountered. The driver will depress the gas pedal to maintain the speed (increase
the torque). Eventually, the engine will have trouble maintaining the needed power due
to its limited torque range and the operating point will drift across the shifting boundary
to point y. Then the shifting controller requests a downshift. In the lower gear, the
engine speed increases and the torque needed drops. Thus, the operating point returns to
the stable region (at z). In general, more than one downshift may be needed for the
engine to keep the operating point in the stable region. The upshift scenario (e.g. going
19
downhill) is similar, but for this case, the operating point crosses from region B up to
region A.
3.2.1.4 Calculating the Vehicle Motion
To figure out the car's velocity profile against time, the program first has to
decide the car's acceleration rate: accelerating; cruising at a constant speed; decelerating
for a traffic light (using brakes); or decelerating by coasting (i.e. for a slower speed limit).
This decision is based on the vehicle's current conditions, speed limit, etc., and the
location of up-coming stops.
Let us consider the simple case where the car accelerates from rest and the next
stop is far away enough to provide ample room to reach a specified cruising speed, cruise
for a while, and finally decelerate to the stop. Figure 3.4 shows a generic acceleration
profile to reach the target speed and the corresponding speed in the acceleration part of
this journey.
20
Typical Acceleration Profile
4.5
----_---
4.0
50.0
-
45.0
-_am-
40.0
3.5
i
a)
E
3.0
- - -+--- Acceleration
35.0
-----
30.0
Velocity
2.5
Co
25.0
0 2v4tc
0
2.0
7E
1.5
20.0
-
10.0
0.5
5.0
1i
0
2
0
15.0
1.0
0.0
.
e
4
6
8
10
12
0.0
14
Time (sec)
Figure 3.4: A representative acceleration profile. This figure shows the profile followed
to reach the target velocity, v,= 4 5 mph. Here, the maximum acceleration, am, reached is
4.5 mph/sec. It takes T=3 seconds to reach this level. The acceleration rate falls at time,
t, when the velocity reaches vC.
The first part of the acceleration profile follows an offset cosine curve:
a(t) =
a
'" [1 -
2
tc
cos(-)]
where
0 < t <;z
I
(1)
so that the maximum acceleration, am, is reached at a predetermined time, t. For the
second part of the acceleration, after time r, the acceleration is fixed at am and the speed
increases linearly with time.
At a certain time, t, (to be defined later), the acceleration tapers off in the third
part of the acceleration profile. This last part follows the second half of the cosine curve,
which is designed to have the same duration, t, as the initial acceleration build up and is
now represented by:
21
a
t -t
' [+ cos(
2
a(t) =
'
-rc)] where tc < t ; t + 1
(2)
The objective is that the vehicle speed should reach the target speed, v,, at the end of the
acceleration profile. Thus, the velocity, v, at the switching time, t, may be solved from:
tc +1
v,
=VC
j-a"' [1+cos( t -t
+
2
-r)]
7 -dt
(3)
1
tC
vC = v,
a.(4
2
The procedure is to keep track of the velocity, v, until v = vc; then the acceleration tapers
off. Normal values of a
=
4.5 mph/s and t =3 seconds are used. These settings give
realis'tic profiles that match practical driving.
This strategy is used unless the required torque reaches the maximum torque
output of the engine; then the acceleration is recalculated according to the maximum
available torque. The calculations for this scenario are covered at the end of section
3.1.2.5.
Consider the case where the vehicle approaches a stretch of road where speed
limit increases. When this occurs, the same acceleration profile is followed, except now
the starting velocity is non-zero.
When the speed limit decreases and there is ample road space ahead (no stopping
point), the vehicle will coast to the lower speed. The value for am is now negative (-1
mph/s), but the above procedure still holds true.
Now, assume the vehicle has reached a cruising speed and a stopping point is
approaching. The deceleration profile for braking to a stop is similar to the acceleration
22
profile except that am is now negative, set at -6 mph/sec, and the target velocity is zero.
In order to stop the car at (or slightly before) the stopping point, the distance required to
stop, x, from the current velocity, v, must be approximated by:
V
2
x
=-
(5)
This follows from:
x
= ffa(t) -dt
(6)
For these calculations, the acceleration rate, a(t), is assumed to be constant at am to avoid
complicated double integrals of the piecewise acceleration profile. Thus:
x =--a, -t +v -t
2
(7)
The time to reach this distance, t, can be calculated by:
v= a(t)-dt
t -
a,
(8)
(9)
Substituting equation (9) into (7) results in the stopping distance, x, shown in (5). When
the next stop location equals this stopping distance, a stop is requested.
Now consider the case where two stopping points are close together. It is possible
that the cruising speed is never reached before a deceleration is required to stop the car.
Since the model constantly calculates the distance required to stop the car from its current
velocity, the above procedure still holds true. In the case that the car must decelerate for
a stop, the acceleration profile is interrupted, and the deceleration profile is begun.
23
Each type of acceleration/deceleration has its own maximum value and time to
reach that value, t. In this model, all types of acceleration require t=3 seconds to reach
their respective maximum value. For normal acceleration, the maximum is 4.5 mph/sec;
for braking to a stop, -6 mph/sec; and for gliding to a lower speed, -I mph/sec. When
braking to a stop, the car is assumed to be in neutral and all power for the stop comes
from the brakes, thus, there is no load on the engine.
To make the velocity profile more realistic, a random number generator was used
to vary the target speed that the car aims for. Every 1/5 mile the goal speed is reset
within 15% of the speed limit. This way, a wider variety of accelerations are seen at
different velocities. For example, if the given speed limit is 65 mph, the model will vary
the car's target speed between 55.25 and 74.75 mph. So, at one point, it may be asked to
reach 57 mph, and 1/5 mile later it may be aiming for 70 mph, and 1/5 mile later, 65mph.
Now, with the acceleration known, current velocity and distance can be
determined from basic physics. The time increment used by the model can be dt = 0.25,
0.5, or I second. The '0' subscript indicates the value at the prior time increment.
v = a -dt +vo
1
x = -a -dt 2 + v -dt +x0
2
(10)
(11)
If the car is stopped, it is told to wait for 60 seconds at each light.
3.2.1.5 Calculating the Engine Operating Conditions
The engine speed, rpm, brake power, Pb (W), and torque, T (N-m), can be
calculated from the vehicle information and the road load requirements. The symbols are
24
defined as follows: G.R. is the overall gear ratio, d is the wheel diameter (m), a is the
road angle (degrees), M is the vehicle mass (kg), g is gravity (m/s 2), Pa is the air density
(kg/m 3), a is acceleration (mph/sec), v is vehicle speed (mph), d is the tire diameter (m),
AV is the frontal area (m2), and Cd and C, are the aerodynamic and road drag coefficients.
Note that a can be positive or negative depending on whether the road grade is uphill or
downhill. The relationships between these parameters are as follows. (Terms in the
equations are in the dimensions defined above.)
v -G.R.- 26.82
rpm =
d .x7
(12)
P, =(F,.+ Fd + F, + F,:).v.0.44704
(13)
P - 30
T = ''0
rpm - c
(14)
The different F's are the forces (N) required to overcome road drag, aerodynamic drag,
acceleration, and climbing an incline, respectively:
F, = C. -M -g .cos(a)
Fd=0.5- p, -v 2 -c -A, -1609.32
F1 = M a -0.44704
(15)
Fe = M -g -sin(a)
The engine speed is set to idle if the operating point is calculated to be below idle.
As mentioned before, if the model's torque exceeds the vehicle's maximum
torque, then the motion data must be recalculated based on the maximum torque. In the
following, the equations are written to be dimensionally consistent instead of in the
dimension specific form of equations 12-15. First, find the brake power that can be
produced by rearranging equation 14:
25
_ T -rpmn.7
30
The acceleration is defined by manipulating the relation F a=ma and equation 13 into:
Fa
a
F
M
P
h
F, -F
-F
M
Now, the new velocity of the vehicle and the total distance traveled must be redefined as:
v = a -dt +vo
1
x =--a-dt2 +v-dt+xo
2
3.2.1.6 Determining Emission Levels
When the engine operating conditions (speed, torque) are known, the quasi-static
engine-out emissions at that instant can be determined from the corresponding map. The
current torque and rpm are used to do a two-dimensional interpolation on the engine maps
to find specific fuel consumption, sfc (g/kW-hr), and emission index numbers, El (grams
of emission per 100 grams fuel). This index can be converted into an emission rate
(grams/sec) by using the brake power (kW) and sfc (g/kW-hr).
100
nh, = EI -sfc - PI,- 3 6 0 0
These values are determined second-by-second; all information is written to a file.
26
(16)
3.2.1.7 Gear Shift
The first time step begins in first gear. For the next time step the next gear
requested (if any) must be determined. For the current torque, the speeds for the upshift
and downshift boundaries are interpolated from the gear-shift map (Figure 3.3). If the
current speed lies above the upshift boundary speed, the gear is increased. A downshift
will occur if the engine speed falls below the downshift boundary. Whether further
shifting is required will be determined at the end of the next time step. Cruising may
require upshifts or downshifts since torque varies with the road grades.
3.2.1.8 Repeat
1 After determining the next gear, the above steps are repeated, starting with the
next acceleration rate from the profile and the characteristics of the road at that location.
If the distance reached by the recently calculated time step exceeds the next distance
value, then the distance index will increase and the next distance step will be used. This
continues until the calculated distance reaches the distance given by the last data point of
the road profile.
3.2.2 Using a Prescribed Velocity Profile
When the velocity profile is already defined (such as with the FTP cycle), the
procedure is simplified. The input files are the same as described above, except the road
profile is replaced by a velocity profile, with each data point containing the time,
duration, dt, and velocity (for the FTP, when there is a change in the velocity, dt=1
second). Acceleration and distance can easily be calculated:
27
(v-v0)
-t
(17)
a= dt
x =
adt +v-dt+xo
(18)
From this, power, rpm and torque are calculated as shown in equations 12-15. No
provisions are made if the vehicle's maximum torque exceeds the torque required to
follow the velocity profile. The assumption with the FTP, though, is that all vehicles can
reach the low accelerations requested by the test. Emissions levels and gear selections
also follow the procedures described above. Note that in this case no elevation changes
occur, so power calculations have zero angle and thus no climbing force.
28
Chapter 4 - Results and Discussion
In order to verify that the model properly calculates engine conditions, shifts at
reasonable times and correctly reads the emission maps, the velocity profile from Bag 1
of the FTP was followed (Figure 4.1). The model was also tested with a road profile
following a route from Central Square in Cambridge, MA onto Storrow Drive, then west
on Route 2 until the interchange with Route 128. This required more checks to verify
that it was properly locating stops, following the acceleration profile, etc.
Both procedures produced series of data which contain time, duration,
acceleration, velocity, distance, road angle (in the first case, zero), gear, torque, rpm,
power, emissions and fuel mass flowrate and cumulative masses. This data was loaded
into MATLAB and several different graphs were created to analyze the output.
4.1 Following the Velocity Profile in the Federal Test Procedure (FTP)
The Bag 1 FTP cycles are shown in Figure 4.1. Each sequence of idle,
acceleration, cruise and deceleration is referred to as one cycle; thus there are five cycles
shown in the figure. The first cycle models suburban street driving. The second cycle
models a cruise at highway speeds for several minutes. A level road is assumed.
The corresponding engine power, speeds, and torques required for the test, as
calculated by the model, are shown in Figures 4.2-4.4. The gear shift schedule described
in section 3.2.1.3 is used. Note that the maximum required brake torque is 120 N-in
(Figure 4.3), which is lower than the maximum torque output of the engine (176 N-m).
These graphs also highlight the limited range of operation in the FTP: the power required
29
never exceeds 30 kW (Figure 4.2) and the engine speed barely tops 3000 rpm a few times
(Figure 4.4). Negative brake power and torque indicate the use of brakes to decelerate:
no load is transmitted to the engine.
Velocity Profile of Bag 1 FTP cycle
60
50
40
0E
20
10
0
100
200
300
Time (sec)
500
400
600
Figure 4.1: The velocity profile followed by Bag 1 of the FTP.
Bag 1
30
252015105-
0
0~
M -5
-10
-15
-20
0
100
200
300
Time (sec)
500
400
Figure 4.2: Brake power against time for Bag 1.
30
600
Bag 1
15(
10(
V
50
-50-
-100
-150-
-200
0
100
200
300
Time (sec)
400
500
600
500
600
Figure 4.3: Engine torque against time for BagI.
Bag 1
3500
3000-
2500-
Eg2000-
1500-
1000-
5001
0
100
200
300
Time (sec)
400
Figure 4.4: Engine speed against time for Bag 1.
Figure 4.5 illustrates the vehicle's motion and gear selections for the first 300
seconds. The first (suburban) cycle has an acceleration with a couple minor
decelerations, where downshifts occur. This is followed by the second (highway) cycle
31
where higher speeds are reached. Downshifts are requested to meet the power
requirements of accelerating after cruising.
Bag 1
0
-51
0
_
50
100
150
200
,5
250
0
-
50
0
c:
100
150
200
300
-----
-
250
1
-~----
300
2.-.............................
0
0
(.2-
501530
nnn~inn
+
+4-{If-l
0
50
100
+Il
150
-fill
200
250
300
Time (sec)
Figure 4.5: The first 300 seconds of Bag 1. This illustrates the basic physics of the
vehicle motion (acceleration, velocity, distance traveled as well as gear requested).
After determining that the time data was reasonable (engine speed and torque
within limits, acceptable shift points, etc.), the engine-out emissions were calculated
according to the quasi-static emission maps. Figure 4.6 represents the cumulative
emissions as time progresses. The slopes of each curve indicate the general overall
flowrates of each species. Level spots correspond to no load imposed on the engine and
thus essentially no emissions. In general, larger slopes mark heavy accelerations.
32
Bag 1 Engine Out Cumulative Emissions
21-0
0
100
200
300
400
500
600
100
200
300
400
50 0
600
100
200
300
Time (sec)
400
500
600
15
10 -o
5-0
0
10
0
z
501
0
Figure 4.6: Cumulative emissions from Bag 1.
Trends were sought for the emissions data by graphing the emitted species flow
rates against engine parameters like engine speed, torque, and power. As can be seen in
Figures 4.7-4.10, the predominant relationship found is between the emission flow rates
and the brake power.
The calculated mass flowrate of HC against brake power (Figure 4.7) shows a
good correlation between the two variables. At lower power, the ratio of HC flowrate to
power is greater than it is at higher powers (this can be seen as the quick rise and then
steady incline in the graph). A similar effect is seen with the fuel flowrate in Figure 4.10.
The relationship may be established as follows. If HC and f are the hydrocarbon and fuel
flowrates, then:
33
HC =100 -EIHC -f
=100. EIHC -P, -sfc
Since EIHC is almost flat over the map (Figure 2.3), HC is proportional to Pb with a
proportional "constant" equal to the sfc. At high power, sfc goes down (more efficient
engine), thus the observed change in slope in Figure 4.7.
The CO emission rates are shown in Figure 4.8; the emission increases with the
engine power. Because the operating points of the FTP are within the 100 N-m, 3000
rpm boundary of the engine map, where the EICO is essentially flat, the CO emission rate
versus power behavior reflects mainly the change in sfc. This effect is similar to the HC
behavior as discussed in the last paragraph. The data point scatter around this linear
relationship (below 0.1 g/s CO) in Figure 4.8 is due to interpolation noise. Above this
value there are five points, at -0.1, 0.15, 0.27 and 0.47 g/s, where operating conditions
reach outside the 100 N-m , 3000 rpm boundary and into the enriched zones. This
enrichment results in high sCO values and thus, elevated CO flowrates.
In Figure 4.9, the flowrate of NO also increases with power; there is, however, no
decrease in the slope of the relationship at the higher power range. This behavior is due
to the fact that the EINO is higher at elevated power, thus offsetting the lower sfc there.
The overall effect is that the NO flowrate increases almost linearly with brake power.
34
Bag 1 Engine Out Emissions
0.02
+
+
0.018
+
+4+
+ -+11 +
0.016
0.014
-
+ +-Ii + -
++4111-+
0.012
U)
c,)
C-)
I
0.01
0.008
-HIF
-
0.006 -
I- -*
0.004 -
-t l
0.002 -
'I S'
-20
M
|| |s ||i
|"M
=u
-10
I M!
'lo
m
30
20
10
0
P b (kW)
Figure 4.7: Flowrate of HC emissions against brake power for Bag 1.
Bag 1 Engine Out Emissions
0.5
+
0.45
0.4 F
0.35 F
0.3+
0.25
0
0.2+
0.15++
0.1
0.05[
O' 1 -
-20
ii
mR
-10
20
10
0
30
Pb (kW)
Figure 4.8: Flowrate of CO emissions against brake power for Bag 1.
35
Bag 1 Engine Out Emissions
0.12
-
0.1
++
0.08-
++
20.06
-
0.04
-
0
z
0.02
nLI
-20
II
-10
10
0
20
30
Pb (kW)
Figure 4.9: Flowrate of NO emissions against brake power for Bag 1.
Bag 1
In
U-
0'
-20
i iii i"" "M
-10
i
iiir
0
20
10
30
Pb (kW)
Figure 4.10: Fuel flowrate against brake power for Bag 1.
36
4.2 Following the Road Profile
The route used is as follows (See Figures 3.1 and 3.2 for the map and elevation
profile from TOPO!). Starting in Central Square, the chosen road profile (see Figures
4.11-4.13 for the elevation and velocity profiles graphed in MATLAB) follows Western
Avenue, over the Charles River and onto Storrow Drive (around 300 seconds or 0.5
miles). Up to this point, it is city driving through four stoplights with a speed limit of 35
mph. Storrow Drive has a limit of 50 mph until it meets up with the Fresh Pond
Parkway. At -900 seconds or 3.5 miles, the Fresh Pond Parkway slows down to 35 mph
until the route follows Route 2 past Alewife T station. This first section has a fairly
constant elevation: no drastic changes occur. But after the final stop light at Alewife
(-1100 seconds or 5 miles), the main highway begins. The speed limit increases to 55
mph and at -1200 seconds, a large hill is encountered in the Belmont area. Just over the
top, there is a shorter descent, followed by smaller hills that neither gain nor lose major
elevation. As seen in Figure 4.11, the vehicle speed varies around the given speed limit.
This produces a wider range of accelerations for all velocities which is more realistic to
driving than holding a constant speed.
37
Central Square to 128
E 40
30
o'' 1'
0
1
" % U1 '1
200
I
.
I
400
600
11
j
.i.I±I
800 1000
Time (sec)
1200
1400
1600
Figure 4.11 : Velocity profile requested by the model for travel from Central Square in
Cambridge to the Route 128 interchange on Route 2.
Central Square to 128
350
300!250200-
150 P
100
50
0
-50 0
0
2
2
4
4
6
8
6
8
Distance (miles)
10
12
10
12
Figure 4.12: Elevation Profile against the distance traveled along the route from
Cambridge, MA to Route 128
38
Central Square to 128
350
300250200-
100
150-0
-500
200
400
600
800
1000
Time (sec)
1200
1400
1600
Figure 4.13: Elevation plotted against the time from Cambridge to Routel28.
Most of the graphs of emission mass flowrates versus brake power resemble those
for the FTP Bag 1 profile below -20kW. Above this, though, variations are seen since
the vehicle operating points in this case can exceed 60 kW (Figure 4.14), which is about
double the maximum power in Bag 1, and can exceed speeds of 4000 rpm (Figure 4.16).
The torque required (Figure 4.15) often reaches the car's maximum value of 176 N-m.
Central Square to 128
80
6040Q-
20
0
Q-0cD -20 -40-60
0
200
400
600
800 1000
Time (sec)
1200
1400
1600
Figure 4.14: Brake power requested to follow the route from Cambridge to Route 128.
39
Central Square to 128
200
100
0
E
-100
-200
-300-
-400
0
200
400
600
800
1000
Time (sec)
1200
1400
1600
Figure 4.15: Engine torque requested to follow the route from Cambridge to Route 128.
Central Square to 128
5500
5000450040003500
E.3000
2500
2000
1500
1000
500
0
200
400
600
800 1000
Time (sec)
1200
1400
1600
Figure 4.16: Engine speed (rpm) requested to follow the route from Cambridge to Route
128.
Figure 4.17 shows the vehicle behavior for five accelerations with four decelerations in
between. The first two accelerations reach constant speeds that require fourth gear. In
40
the third and fourth acceleration, the car reaches a higher speed, but immediately
decelerates for a stop. Because of the acceleration, the torque required is much higher
than it would be for cruising. Thus, the engine operating conditions never cross the
upshift boundary in Figure 3.3 and a gear past second is never requested. The fifth
acceleration brings the vehicle to a cruising speed but, just past 350 seconds, an
acceleration requires two downshifts to provide enough power.
Central Square to 128
.50
0i
50
100
150
200
250
390
350
400
0
50
100
150
200
250
300
350
400
50
100
150
200
250
300
350
400
00
0
>V
0
O_
1-r
-I--..?*
I. .........
..............
0.....
0
0
'--"
50
,
*
..
II
100
150
I
200
If~
250
I
----
300
I--
350
400
Time (sec)
Figure 4.17: The first 400 seconds of the route from Cambridge to Route 128. This
illustrates the basic physics of the vehicle motion (acceleration, velocity, distance
traveled as well as gear requested).
Figure 4.18 illustrates the cumulative emissions. At 1200 seconds, when the
vehicle is climbing the hill in Belmont, a large slope is seen in the graphs. After the top
is reached, the slope decreases (- 1300 seconds), indicating a lower emission flowrate due
41
to the decrease in power requirements. The large jumps seen in the CO graph correlate to
very high flowrates due to enrichment for high torques and rpms. The slopes of the NO
graph are more subdued because enrichment at higher torques and rpm reduces the NO
flowrate.
Cambridge Engine Out Cumulative Emissions
10
5
-
01
0
200
400
600
800
1000
1200
1400
0
o0100
0----330-0
40
60
80
100
10
40
0
200
400
600
800
1000
1200
1400
1600
200
400
600
800 1000
Time(sec)
1200
1400
1600
1600
300
10
320
0
z 1001
0
Figure 4.18: Cumulative emissions for the route from Cambridge to Route 128.
Now consider the plots of emission flowrates versus brake power in Figures 4.194.22. Major deviations from the corresponding graphs from the FTP data occur. The
variations from a linear relationship for CO are seen in Figure 4.19. As power exceeds 30
kW, enrichment that occurs at high torque and rpm causes the CO emissions to reach up
to 4 g/s. The fairly linear relationship that remains below 0.2 g/s CO are for operating
conditions that remain within the 100 N-m and 3000 rpm boundary (refer to Figure 2. id).
42
The "wild" data points above the linear relationship are the result of engine conditions
outside this boundary. Otherwise, under 20 kW, the graph is a good duplicate of the Bag
1 graph (Figure 4.8).
A similar deviation from the linear can also be seen with the HC emissions
(Figure 4.20). But in this case, the values of sHC don't have as wide a range as sCO.
This limits the spread of the HC flowrate as power increases. Below 30 kW, though, a
concave down relationship, similar to the Bag 1 graph (Figure 4.7), can still be seen.
Figure 4.21 shows that for stoichiometric mixtures, the relationship for NO
flowrate resembles the Bag 1 graph, Figure 4.9. The points that deviate below this line
are the result of lower sNO values at torques above 110 N-m as predicted by the sNO
map in Figure 2.4b. In this region, high enrichment occurs, greatly reducing the NO
emissions. This occurs particularly when accelerating up the large hill in Belmont.
Figure 4.22 closely resembles the corresponding graph for fuel flowrate versus
brake power for Bag 1 (Figure 4.10). The only difference being that the power surpasses
30 kW and reaches 70 kW while still maintaining the linearity of the flowrate.
43
Cambridge Engine Out Emissions
2-
+ +
0.
-60
-40
-20
0
20
Pb (kW)
40
60
80
Figure 4.19: Flowrate of CO emissions against brake power for the Cambridge route.
Cambridge Engine Out Emissions
0.07
0.06
0.05
0.04
CD)
0
0.03
0.02
0.01
-60
-40
-20
0
20
Pb (kW)
40
60
80
Figure 4.20: Flowrate of HC emissions against brake power for the Cambridge route.
44
Cambridge Engine Out Emissions
0.1
-0.08-
+++
+
~++
0
+
Z0.06
#
++
+
0.04
+++
0.02-
0
60
*
++
n HH001
-20
-40
+
+
++E
0
20
Pb (kW)
40
60
80
Figure 4.21: Flowrate of NO emissions against brake power for the Cambridge route.
Cambridge
4.5
+ + *
4-
-
3.5.
~
.++
3
2.5-
1.5-
0.5
0
-60
-40
-20
20
0
Pb (kW)
40
60
80
Figure 4.22: Fuel flowrate against brake power for the Cambridge route.
4.3 Conclusions
In this stage of the project, the main goal was to develop a model to create the
time sequence of a vehicle's operating conditions and corresponding emissions from a
given road profile. The models used to select gears and calculate the engine conditions
45
follow an acceptable profile. Shifting points are reasonable and engine conditions are
within expected operating conditions. By using quasi-steady engine-out emission maps,
the basic function of the emission model was verified. The basic relationship of
increasing emissions mass flowrates with power was followed for the majority of the
species (as well as for the fuel mass flowrate). Also, the relationships between the CO
and NO flowrates and enrichment (due to the engine control demands at high torque and
rpm) were followed.
The next step is to determine how this quasi-steady emission profile is related to
an actual emission profile for the same route. By identifying operating conditions where
the emissions differ, the model can be modified to properly reflect real-world emission
characteristics. Possibly there is a relationship between acceleration and flowrates or
maybe the engine speed causes drastically different emission levels when under transient
conditions. These questions are left to be answered in phase 2.
46
Appendix
Appendix A: Ford Contour Specifications
C
Cd
Mass
Frontal Area
Wheel Diameter
Displacement
Maximum Torque
Idle
Maximum rpm
Number of Gears
Final drive ratio
First G.R.
Second G.R.
Third G.R.
Forth G.R.
.015
.4
1258 kg
2.4 m2
.6146 m
.002 m3
176 N-m
750 rpm
6000 rpm
4
3.92
2.89
1.57
1.00
.7
47
Appendix B: Data File Formats
Car Specifications:
This is the format for the Contour information. The first line contains the drag
coefficients, the mass, frontal area, wheel diameter, and engine displacement. Line 2 is
the maximum brake torque, idle speed and maximum rpm. Line three contains the
number of gears and the final drive ratio. The last lines are the transmission gear ratios.
.015 .4 1258 2.4 .6146 .002
176
750
6000
4 3.92
2.89
1.57
1.00
.7
Shifting schedule:
The first line contains the normalized torque values (the x-axis in Figure 3.3). The
second line contains the upshift boundary points in terms of the normalized engine speed
(the solid line in the figure). Accordingly, the third line is the downshift boundary (the
dashed line in the figure).
-0.1
0
0.1
0.2
0.254 0.254 0.254 0.291
0.128 0.128
0.3
0.4
0.5
0.6
0.7
0.8
0.365 0.465 0.579 0.695 0.803 0.891
0.9
1
0.947 0.960
0.137 0.152 0.173 0.199 0.230 0.264 0.300 0.339 0.379 0.419
Pixel profile:
This is the beginning of the Cambridge to Route 128 pixel profile created from ImagePro
Plus. The first line contains the number of pixel points in the file. Line 2 is the ratio of
the x-axis: in this case there are 67 pixels per 1 mile. Accordingly, line 3 shows the
elevation scale as 62 pixels per 50 feet. The rest of the lines contain the location of the
pixels in the profile. The first number is the number of pixels from the left side of the
image; the second number is the number of pixels from the top of the image (larger
numbers indicate lower elevations).
708
1 67
5062
44
45
46
424
424
424
47
425
48
49
50
425
425
425
48
Stop locations and speed limits data:
The first line is the number of stops along the route. The next lines within that number
contain the mileage where each stop is located. The next line after these is the number of
speed limit changes. Each line after that has the mileage and the new speed limit at that
point. (The first mileage must be zero in order to assign the first speed limit.)
11
.17
.35
.45
.53
1.93
2.17
2.33
2.68
3.58
3.83
4.05
4
035
.57 50
3.15 35
4.13 55
Route profile:
This is the beginning of the route from Cambridge to Route 128, created from the pixel
data and the stopping point data. The first line contains the number of data points in the
file and the distance increment. The rest of the lines contain the distance traveled in
miles, the elevation above the starting point in feet (a negative indicates an elevation
below the starting point), a flag to indicate a stop location (a 0 indicates a stop), and the
speed limit at that point in mph.
709 .014925373134
.000000000000 0. 1 35
.014925373134 0. 135
.029850746269 0. 1 35
.044776119403 -1. 1 35
.059701492537 -1. 1 35
.074626865672 -1. 1 35
.089552238806 -1. 1 35
.104477611940 -1. 1 35
.119402985075 -1. 1 35
.134328358209 -1. 1 35
.149253731343 -2. 1 35
.164179104478 -2. 1 35
.179104477612 -2.035
49
.194029850746
.208955223881
-2. 1 35
-2. 1 35
Velocity profile:
This is the beginning of Bag 1. The first line contains the number of data points and the
standard time increment. Each line thereafter contains the time in seconds, the duration at
that point and the speed in mph.
403
1
20
21
22
23
24
25
26
27
28
29
30
31
1
1
19
1
1
1
1
1
1
~1
0
0
1.5
4.4
7.2
10.1
12.9
15.6
17.1
17.7
19.4
21.2
22
Emission Maps:
This contains the emission maps. The first line is the size of the matrix (in this case,
4x4). The second line contains the rpm values for the matrix (the x-axis) and the second
line contains the torques (the y-axis). Since it is 4x4, there is a new data type every 4
lines. There are 4 sets of data: sfc, EIHC, EICO, and EINO. Speed increases across each
line, and torque increases from the first line to the fourth in each set. The zeros are fillers
in case the matrix is larger.
4
1500
36
346.87
286.35
247.12
294.37
1.26
1.21
1.11
1.35
6.39
3.5
4.12
45.3
2000 3000 4000
70
105
140
363.92 358.20 370.48
272.50 265.90 281.97
237.59 228.46 245.67
277.94 220.04 223.44
1.09
1.24
1.09
1.15
1.01
1.09
1.04 0.925 1.26
1.22 1.07
1.14
6.4
5
6.41
4.94 5.01 37.5
4.98 4.97 44.9
51.3 42.2 68.8
50
2.28
4.32
4.7
1.34
2.14
4.58
5.19
1.23
4.05
5.66
6.04
2.22
4.43
3.21
2.28
0.886
0
0
0
0
0
0
0
0
0
0
0
0
51
0
0
0
0
0
0
0
0
0
0
0
0
Appendix C: Fortran Code
The following pages contain the FORTRAN code for the model. The main program is
presented first; the subroutines follow in alphabetical order. To change the input files
used by the model, the subroutine 'openfiles' was edited.
52
program profiler
C*Todd Haugsjaa
C*The purpose of this program is to take data in the format of
C*distance, elevation, whether or not there is a stop light at each
C*distance increment and the speed limit and transform it into a
C*velocity profile against 1 second increments.
From this, brake
C*power, gear and engine speed and emission levels are determined.
C*
C*It assumes a sinusoidal acceleration and deceleration to calculate
C*the velocity profile and assumes that the car is capable of
C*producing the correct power (which is calculated from velocity,
C*accel,etc.).
C*
C*It is also possible to follow a prescribed velocity profile with no
C*elevation changes.
C*
C*DATA IN RELATION TO DISTANCE TRAVELED, d
C*y=elevation (ft)
C*light=l if no light, =0 when the car should stop
C*limit=speed limit (mph)
C*dd=the distance increment between readings (mi)
C*alpha=angle(degrees) calculated from elevation change and dd
real d(5000),y(5000),light(5000),limit(5000),dd,alpha(5000)
C*CAR DATA
C*ratio=array of gear ratios
C*Cr=coeff of rolling friction
C*Cd=coeff of aero. drag
C*M=mass of car (kg)
C*Area=frontal area of car
(m^2)
C*diameter=tire diameter (m)
C*displacement=engine displacement volume (m^3)
C*nogears=number of gears on car
C*torquemax is the car's maximum producible torque
C*rpmmax is the car's maximum producible engine speed
C*pertorque contains an array percentage of maximum torques
C*up and dn are the engine speeds where a shift is requested for
C*
12 torques referenced from pertorque
C*idle is generally the lowest engine speed
real ratio(5),Cr,Cd,M,Area,diameter,displacement
integer nogears
real torquemax,pertorque(12),
&
idle,rpmmax,up(12),dn(12)
C*DATA IN RELATION TO TIME, time (sec)
C*duration=the length
of time spent at
each value (sec)
C*a=acceleration of car (mi/hr^2)
C*v=velocity (mph)
C*x=distance traveled
C*Pb=brake power (W)
C*rpm=engine speed
(mi)
(rpm)
C*bmep=brake mean effective pressure
C*torque=brake torque (N-m)
C*gear=what gear the car is in
real time,duration,a,vx,Pb,
&
rpm,bmep,torque
integer gear
53
(Pa)
C*DATA FOR READING VELOCITY PROFILE's
real
(BAGs)
time2(5000),duration2(5000),v2(5000)
C*EMMISIONS
C*mrpm=map rpm (in percentage of total)
C*mload=map torque
(in
percentage of total)
C*grid=grid size of emission map (4 means 4X4)
C*sfc=map spec fuel cons (g/kWhr)
C*sfhc=map specific emissions(g/kWhr)
C*eihc=map (% hc/fuel)
real mrpm(10),mload(10),sfc(10,10),
&
&
sfhc(10,10),sfco(10,10),sfno(10,10),
eihc(10,10),eico(10,10),eino(10,10)
integer grid
C*INCREMENTING,etc.
C*n=number of distance data points
C*t=number of time data points for velocity profile
C*files=l
(bag)
for default files;=O for user entered
C*dt=increment
between time data
(.25
.5 or
1 sec)
C*velprof=y for reading velocity profile (bag)=n for distance profile
integer n,t
real dt
character (1) velprof
C**************** ****
****************************
**********
call openfiles(velprof,dt)
call readfile(n,dd,d,y,light,limit,Cr,Cd,M,Area,
diameter,displacement,nogears,ratio,
&
torquemax,rpmmax,pertorque,up,dn,idle,
mrpm,mload,velprof,time2,duration2,v2,t,dt,
&
grid,sfc,eihc,eico,eino)
&
if (velprof.eq.'n') then
call compute(nogears,ratio,d,y,dd,limit,light,
&
n,dt,Cr,Cd,M,Area,diameter,displacement,
&
torquemax,rpmmax,pertorque,up,dn,idle,
&
mrpm,mload,grid,sfc,eihc,eico,eino)
else
call compute2(v2,nogears,ratio,
&
time2,duration2,dt,Cr,Cd,M,Area,diameter ,displacement,
&
torquemax,rpmmax,pertorque,up,dn,idle,t,
&
mrpm,mloadgrridsfc
eihc eico ei no)
endif
end
program
54
subroutine compute(nogears,ratio,d,y,dd,limit,light,
&
n,dt,Cr,Cd,M,Area,diameter,displacement,
&
torquemax,rpmmax,pertorque,up,dn,idle,
&
mrpm,mload,grid,sfc,eihc,eico,~eino)
C*This is the main computing routine - it turns a distance profile
C*into a requested velocity profile by following an acceleration
C*profile.
It then calculates the engine speed, torque and brake
C*power required to follow that.
A call to requestgear is made to
C*figure out which gear the car should be in.
C*Also, emission levels are determined through a call to a subroutine
C*max, min and coast variables indicate peak acceleration (mi/hr^2)
C*and the time required to reach that peak (sec). For accelerating,
C*braking, and coasting to slow down, respectively.
real amax,tmax,amin,tmin,acoast,tcoast
C*DISTANCE DATA
real d(5000),y(5000),light(5000),limit(5000),dd,
alpha(5000),height,angle
&
C*TIME DATA
real time,duration,a,v,x,Pb,rpm,bmep,torque
C*CAR DATA
C*row=air density (Pa)
C*g=gravity (m/s^2)
real ratio(5),Cr,Cd,M,Area,diameter,displacement,row,g
real torquemax,rpmmax,pertorque(12),up(12),dn(12),idle
integer gear,nogears
C*variables for emissions
C*mrpm and mlaod are the map values of the engine speed and load
C*sfhc, sfco, sfno values are calculated (g/kWhr)
C*hc,co,no,fuel (g/s) and cumulative (grams) numbers are calculated
C*sfc and ei values are from the maps
C*grid=the grid size of the maps. (e.g. if grid=4, then it is a 4x4
C*matrix of points
real mrpm(10),mload(10),
&
sfc(10,10),fuel,cummfuel,
sfhc(10,10),hc,cummhc,
&
sfco(10,10),co,cummco,
&
&
sfno(10,10),no,cummno,
&
eihc(10,10),eico(10,10),eino(10,10)
integer grid
C*INCREMENTERS AND FLAGS
C*stopped is used to indicate if the car has stopped after a stop
C*has been requested (needed since it can take 2 or more
C*distance increments)
C*j=distance data incrementer
C*status=-2,-1,0,1 for braking,coasting,cruising,accelerating
C*int=interval: how far along the acceleration sine wave
logical stopped
integer j,status,n
real dt,int
C*USED TO FIND UP COMING STOPS
C*k=data location of next stop
C*stoplocation=distance data point where car can physically stop
55
integer k
real stoplocation,ki
row=1.2
g=9.81
amin=
tmin=
amax=
tmax=
acoast=
tcoast=
-6*3600
3
4.5*3600
3
-1*3600
3
C*first increment is set as follows:
time=0
duration=dt
x=0
v=0
a=0
Pb=0
rpm=idle
gear=1
bmep=0
torque=0
cummhc=0
j=2
alpha(j)=asind((y(j)-y(j-1))/dd/5280)
,angle=alpha(j)
height=y(j)
call emissions(mrpm,mload,a,rpm,
&
torque,duration,Pb,rpmmax,torquemax,
&
grid,eihc,hc,cummhc,eico,co,cummco,eino,no,cummno,
&
sfc,fuel,cummfuel)
call writefile(time,duration,x,v,a,angle,Pb,gear,rpm,
&
bmep,torque,hc,cummhc,co,cummco,no,cummno,light(l),height,
&
fuel,cummfuel)
call nextstop(k,j,n,light)
C*this prevents a crash at the end of the route
y(n+l)=y(n)
int=0
status=1
do while (j.le.n)
alpha(j+l)=asind((y(j+l)-y(j))/dd/5280)
do while (x.le.d(j))
stoplocation=(-(v**2)/(2*amin)+x)
if ((stoplocation.ge.(k-2)*dd).and.(k.ne.n))then
C*start deceleration
stopped=.false.
status=-2
else
stopped=.true.
endif
call finda_vIx(stopped,status,limit,int,dt,amin,acoast,
amax,tmin,tmax,tcoast,a,v,x,j,kn,time,duration,light,
&
&
dd,angle,alpha,height,y,torquemax,Pb,Cd,Area,g,M,Cr,row,
&
d,rpm,ratio,idle,diameter,gear,torque)
call emissions(mrpm,mload,a,rpm,
&
torque,duration,Pb,rpmmax,torquemax,
56
&
&
grid,eihc,hc,cummhc,eico,co,cummco,eino,no,cummno,
sfc,fuel,cummfuel)
C*This makes values more neutral for the time at a stop by inserting
C*another set of time data containing the values required to reach
C*that stop and giving the duration of the stop zero values for
C*engine conditions, etc.
if (duration.gt.dt) then
time=time-duration+dt
call writefile(time,dt,x,v,a,angle,Pb,gear,rpm,
&
bmep,torque,hc,cummhc,co,cummco,no,cummno,light(j),
&
height,fuel,cummfuel)
time=time+duration
Pb=0
torque=0
bmep=0
a=O
endif
C
&
&
print*,
&
enddo
call writefile(time,duration,x,v,a,angle,Pb,gear,rpm,
bmep,torque,hc,cummhc,co,cummco,no,cummno,light(j),
height,fuel,cummfuel)
v,a,status,stopped,light(j)
call requestgear(torque,rpm,v,torquemax,rpmmax,
pertorque,up,dn,gear,status,nogears)
j=j+l
enddo
C*convert mi/gram into
mpg (density
=750 g/L)
cummfuel=x/cummfuel*750*3.785
print *,'fuel mileage for the trip: ',cummfuel
close(8)
return
end
57
subroutine compute2(v2,nogears,ratio,
&
&
&
time2,duration2,dt,Cr,Cd,M,Area,diameter,displacement,
torquemax,rpmmax,pertorque,up,dn,idle,t,
mrpm,mload,grid,sfc,eihc,eico,eino)
C*This turns a velocity profile into
C*acceleration, brake power, etc. A call to requestgear is made to
C*figure out which gear the car should be in.
C*TIME DATA
real time2(5000),duration2(5000),a,v2(5000),x,Pb,
rpm,bmep,torque,angle,height
&
C*CAR DATA
C*row=air density (Pa)
C*g=gravity (m/s^2)
real ratio(5),Cr,Cd,M,Area,diameter,displacement,row,g
real torquemax,rpmmax,pertorque(12),up(12),dn(12),idle
integer gear,nogears
C*INCREMENTERS AND FLAGS
C*i=time incrementer
C*j=distance data incrementer
C*status=-1,0,1
for
braking,cruising,accelerating
integer i,status,t
,real dt
C*VARIABLES FOR EMISSIONS (described in compute.for)
real mrpm(10),mload(10),
&
sfc(10,10),fuel,cummfuel,
&
sfhc(10,10),hc,cummhc,
&
&
sfco(10,10),co,cummco,
sfno(10,10),no,cummno,
&
eihc(10,10),eico(10,10),eino(10,10)
integer grid
row=1.2
g=9.81
C*first increment is set as follows:
i=1
x=O
a=0
Pb=0
rpm=idle
torque=0
Pb=0
bmep=0
gear=1
cummhc=0
angle=0
height=0
status=1
C*dummy variable for velocity profile
light=1
call emissions(mrpm,mload,a,rpm,
&
torque,duration2(i),Pb,rpmmax,torquemax,
58
&
&
grid,eihc,hc,cummhc,eico,co,cummco,eino,no,cummno,
sfc,fuel,cummfuel)
call
&
&
writefile(time2(i),duration2(i),x,v2(i),a,angle,Pb,
gear,rpm,bmep,torque,hc,cumrnmhc,co,cummco,no,cummno,light,
height,fuel,cummfuel)
do while
(i.lt.t)
i=i+l
C*present
conditions(i)
are a
result
of past
conditions
(i-1)
a=(v2(i)-v2(i-1))/dt*3600
x=.5*a*(dt/3600)**2+(v2(i)*dt/3600)+x
if (a.lt.0) then
status=-1
elseif
(a.gt.0) then
status=l
else
status=0
endif
(gear) /3.
rpm=v2 (i) *ratio
if (rpm.lt.idle) then
14159/diameter*26.8224
rpm=idle
endif
Pb=(Cr*M*g*cosd(angle)+
.5*row*(v2(i)*.44704)**2*Cd*Area+
&
&
M*a*1.2418e-4+M*g*sind(angle))*v2(i)*.44704
torque=Pb/rpm/(3.14159/30)
emissions (mrpm,mload,a,rpm,
,call
torque,duration2(i),Pb,rpmmax,torquemax,
&
grid,eihc,hc,cummhc,eico,co,cummco,eino,no,cummno,
&
sfc,fuel,cummfuel)
& .
writefile(time2(i),duration2(i),x,v2(i),a,angle,Pb,
call
gear,rpm,bmep,torque,hc,cummhc,co,cummco,no,cummno,light,
&
height,fuel,cummfuel)
&
(torque, rpm,v2 (i) ,torquemax, rpmmax,
requestgear
call
&
pertorque,up,dn,gear,status,nogears)
enddo
cummfuel=x/cummfuel*750*3.785
print *,'fuel
close(8)
return
end
mileage
for the trip:
59
',cummfuel
subroutine emissions(mrpm,mload,a,rpm,
&
torque,duration,Pb,rpmmax,torquemax,
&
grid,eihc,hc,cummhc,eico,co,cummco,eino,no,cummno,
&
sfc,fuel,cummfuel)
C****************************
C*
C*
****************************************
This determines the emission level for each dt in
grams/sec based on the engine speed and load.
C*data against time
real a,rpm,torque,duration,Pb
C*incrementers
and constants
integer j,k
C*engine vales
C*max indicates the engines upper limits
C*ratio indicates the current ratio of rpm or toruqe to its max value
real rpmmax,torquemax,rpmratio,torqueratio
C*variables for emissions
(described in compute.for)
real mrpm(1O),mload(10),
&
sfc(10,10),fuel,cummfuel,
&
eihc(10,10),hc,cummhc,
&
eico(10,10),co,cummco,
&
eino(10,10),no,cummno
,integer
grid
* ***
C*****************************************
*****
********
rpmratio=rpm/rpmmax
torqueratio=torque/torquemax
j=2
do while
((rpmratio.gt.mrpm(j)).and.(j.lt.grid))
j=j+1
enddo
k=2
do while
((torqueratio.gt.mload(k)).and.(k.lt.grid))
k=k+l
enddo
call interpolemiss(rpmratio,mrpm,torqueratio,mload,
&
eihc,j,k,hc)
call interpolemiss(rpmratio,mrpm,torqueratio,mload,
&
eico,j,k,co)
call interpolemiss(rpmratio,mrpm,torqueratio,mload,
&
eino,j,k,no)
call interpolemiss(rpmratio,mrpm,torqueratio,mload,
&
sfc,jk,fuel)
if
(Pb.gt.0) then
C*creates (g/s) from the
C*and sfc(g fuel/kWhr)
emiss index
(g emm/100g
fuel)
hc=(hc/100)*fuel*Pb/1000/3600
co=(co/100)*fuel*Pb/1000/3600
no=(no/100)*fuel*Pb/1000/3600
C*creates
g/s
from g/kWhr
fuel=fuel*Pb/1000/3600
else
C*if negative power,
hc=0
then no emissions
60
from engine
co=O
no=O
fuel=0
endif
cummhc=cummhc+hc*duration
cummco=cummco+co*duration
cummno=cummno+no*duration
cummfuel=cummfuel+fuel*duration
return
end
61
subroutine finda_v-x(stopped,status,limitint,dt,amin,acoast,
&
amax,tmin,tmax,tcoast,a,v,x,j,k,n,time,duration,light,dd,
&
angle,alpha,height,y,torquemax,Pb,Cd,Area,g,M,Cr,row,d,
&
rpm,ratio,idle,diameter,gear,torque)
C*This varies the goal speed requested and calculates the physics of the
C*vehicle and engine conditions.
USE MSFLIB
logical stopped
integer status,j,k,n,jinc
real limit(5000),light(5000),int,dt,time,duration,
&
amin,acoast,amax,tmin,tmax,tcoast,
&
a,v,x,dd,torquemax,Pb,angle,alpha(5000),height,y(5000),Cd,Area,
&
g,M,Cr,row,d(5000),rpm,ratio(5),idle,diameter,
ranval,variation
&
integer gear
C***************
********
******
************
C*this if-then will vary the speed limit (possibly imposed by traffic)
C*The 'call seed' will vary the random sequence each time the program is
run ,
call seed (RND$TIMESEED)
C
C*variation is the percentage deviation allowed around the speed limit
variation=.15
C*jinc is the number of j's between changes.
C*In this case, about every .2 miles
jinc=nint(.2/dd)
if (mod(j,jinc).eq.0) then
call random(ranval)
limit(j)=((ranval*2-1)*variation+l)*limit(j)
else
limit(j)=limit(j-1)
endif
if (.not.stopped) then
status=-2
C*it may take more than two distance increments to stop
else
if (v.lt.limit(j)) then
status=1
else if
(v.gt.limit(j)) then
status=-1
else
status=O
endif
endif
C*this case will make calls to find the acceleration requested
select case (status)
case (1)
call rate(amax,tmax,a,v,limit(j),int,dt)
case (0)
a=0
case (-1)
call rate(acoast,tcoast,a,v,limit(j),
62
&
int,
dt)
case
(-2)
call rate(amin,tmin,a,v,0.0,int,dt)
endselect
v=v+a*dt/3600
x=.5*a*(dt/3600)**2+(v*dt/3600)+x
C*If the physics take the vehicle beyond the current distance
C*increment, the next increment is used to calculate the engine
C*conditions.
if (x.gt.d(j)) then
angle=alpha(j+1)
height=y(j+l)
else
angle=alpha(j)
height=y(j)
endif
rpm=v*ratio(gear)/3.14159/diameter*26.8224
if (rpm.lt.idle) then
rpm=idle
endif
Pb=(Cr*M*g*cosd(angle)+
&.5*row*(v*.44704)**2*Cd*Area+
&M*a*1.2418e-4+M*g*sind(angle))*v*.44704
torque=Pb/rpm/(3.14159/30)
C*if the torque requested exceeds the maximum torqe
C*the car can produce, the acceleration is limited
C*by the max torque, and the car may slow down
if (torque.gt.torquemax) then
torque=torquemax
Pb=torque*rpm*3.14159/30
a=(Pb/v/.44704
&
-Cr*M*g*cosd(angle)
&
-. 5*row*(v*.44704)**2*Cd*Area
&
-M*g*sind(angle))/M/1.2418e-4
v=a*dt/3600+v
x=.5*a*(dt/3600)**2+v*dt/3600+x
endif
if (v.le.2e-4) then
v=0
duration=60
stopped=.true.
status=1
call nextstop(k,j,n,light)
else
duration=dt
endif
time=time+duration
return
end
63
subroutine interpolate(il,i2,xlx2,i3,x3)
C*
ii
i3
12
C*
x1
x3
x2
C*The object is to find x3
real xl,x2,x3,il,i2,i3
x3=xl+(i3-il)/(i2-il)*(x2-xl)
return
end
64
subroutine interpolate2d(il,i2,jl,j2,xl,x2,x3,x4,i5,j5,x5)
C*
C*
C*
C*
C*The
ii
i3
x5a
x2
j5
x5
j2
x3
x5b
x4
object is to find x5 after finding x5a and x5b
ji
i5
x1
C************
********************************************
real il,i2,i5,jl,j2,j5,xl,x2,x3,x4,x5,x5a,x5b
****
****************************************************
call
interpolate(il,i2,x1,x2,i5,x5a)
call interpolate(il,i2,x3,x4,i5,x5b)
call interpolate(jl, j2,x5a,x5b,j5,x5)
return
end
65
subroutine interpolemiss(rpmratio,mrpm,torqueratio,mload,
&
memiss,j,k,emiss)
C*This
feeds
the emission levels
into
the interpolate2d
subroutine
real rpmratio,mrpm(10),
torqueratio,mload(10),
&
memiss(10,10),emiss
&
integer j,k
real xl,x2,x3,x4,x5,il,i2,i5,jl,j2,j5
xl=memiss(j-l,k-1)
x2=memiss(i,k-1)
x3=memiss(j-l,k)
x4=memiss(i,k)
i 1 =mrpm (j-1)
i2=mrpm(j)
jl=mload(k-1)
j2=mload(k)
i5=rpmratio
j5=torqueratio
call interpolate2d(il,i2,jl,j2,xl,x2,x3,x4,i5,j5,x5)
\emiss=x5
if (emiss.lt.0) then
emiss=O
endif
return
end
66
subroutine nextstop(k,j,n,light)
integer j,k,n,light(5000)
C*This
C*next
subroutine looks ahead in the distance data to
stop
C*can't have
two consecutive stops in distance data
k=j+2
do while ((light(k).ne.0).and.(k.lt.n))
k=k+l
C
enddo
print *,'stop
return
end
at
',k
67
find the
subroutine openfiles(velprof,dt)
C*This subroutine asks which files are to be used by the program
C*and whether it will follow a velocity profile or a road profile.
C*If
it is
a road profile, it can convert
from pixels
to distance if
C*needed.
****************************************
C************
integer
real dt
files
character(1) velprof,dopixels
character (30) filenamel, filename2,filename3,filename4,
&
filename7,filename8,filename9
files=1
if (files.eq.1) then
dopixels='n'
velprof='y'
C*time increment, dt,
for
road profile
dt=.5
C*road or velocity profile
filenamel='bagl.txt'
C*car characteristics
filename2='contoura.txt'
must be
.25,
.5
or
1 second
C*shifting
filename3='shifting.txt'
C*emisssions
filename4='conemm.txt'
C*output file
filename8='bagl.out'
else
print *,'is this a velocity profile (ftp-style) [y,n]?'
read(*,*) velprof
print *,'what file has(will have) road profile or velocity
&profile?'
read(*,*) filenamel
print *,'what file has car characteristics?'
read(*,*) filename2
print *,'what file has shifting schedule?'
read(*,*) filename3
print *,'what file has emissions maps?'
read(*,*) filename4
print *,'output to what file?'
read(*,*) filename8
endif
open (1, file=filenamel)
open (2, file=filename2)
open (3, file=filename3)
open (4, file=filename4)
open (8, file=filename8)
if
(velprof.ne.'y') then
if
(dopixels.eq.'y') then
print
*,'what
file has pixel map?'
read(*,*) filename7
open (7, file=filename7)
print *,'what file has stop/limit
read(*,*) filename9
open (9, file=filename9)
call pixel
close(7)
close(9)
68
data?'
rewind (1)
endif
endif
return
end
69
subroutine pixel
C*This reads the pixel outline and creates the road profile.
C*Saved to a file to store stopage and limit info for later runs.
C******** ************************************************************
C*x=distance in pixels
C*y=height in pixels (in distance from top of image!)
C*mi/pixl=distance/pixels used to calculate ratio
C*ft/pix2=height/pixels used to calc ratio
C*xl=first distance (pixels)
C*x2=new pixel distance read (can have multiple y's
for one x
C*
last y)
C*dd=mi/pixl
C*dh=ft/pix2
C*h=height in ft.
C*stops(i)=location of stops in mi
C*location(i)=location of new speed limits
C*limit(i)=speed limit corresponding to location(i)
C*d=current distance in mi
C*n=number of distance data
C*i=incrementer for inserting stops
C*j=incrementer for inserting limits
C*s=number of stops
C*m=number of limits
C*yl=first height in pixels
-
use
,real x,y,mi,pixl,ft,pix2,xl,x2,dh,h,stops(20),location(20),y1
double precision dd,d
integer n,i,j,s,m,limit(20)
C*********
**********
*******
**************
****
C*stop locations read from file
read (9,*) s
i=1
do while (i.le.s)
read (9,*) stops(i)
i=i+1
enddo
C*Speed limits read from file
read(9,*) m
j=1
do while (j.le.m)
read (9,*) location(j),limit(j)
j=j+1
enddo
C*pixel points read
read (7,*) n
read (7,*) mi,
read (7,*) ft,
read (7,*) x1,
dd=mi/pixl
dh=ft/pix2
from file
pixl
pix2
yl
C*first distance increment.
C*difference
d=0
h=0
light=1
actual height doesn't matter, just
70
C*write road profile in miles/feet to new file
write (1,50) n+l,dd
50
100
write (1,100) d,h,light,limit(l)
format (i4,x,f16.12)
format (f16.12,x,f6.0,x,i1,x,i2)
x=xl
x2=xl
i=1
j=1
do while (x2.lt.(n+xl))
read (7,*) x2,y
do while (x2.eq.x)
read (7,*) x2,y
enddo
x=x2
d= (x2-xl) *dd
h=(yl-y)*dh
if
((d.ge.stops(i)).and.(i.le.s))
then
light=0
i=i+l
else
light=1
endif
if
((d.ge.location(j)).and.(j.le.m))
j=j+1
endif
write
,enddo
(1,100)
d,h, light, limit (j-1)
return
end
71
then
subroutine rate(accel,tau,a,v,goal,int,dt)
C*This determines
the acceleration rate based on an acceleration
C*profile chosen to resemble a sine wave.
C*increases until it reaches
Initially, the rate
the max rate at which point
it holds
C*steady until the difference between the goal velocity and the
C*present velocity requires a
slackening of
the rate.
C*accel=the maximum acceleration (or decel) rate
C*tau=the time taken to reach the max acceleration
C*goal=the velocity requested by the speed limit or stop
real accel,tau,a,v,goal,dtint
C*if the direction of acceleration changes
C*the sine curve must restart
(due to close stops,etc.)
if (accel*a.le.0) then
int=0
endif
C*advance the sine wave if below tau or if the goal speed is close
if ((int.lt.tau).or.(int.gt.tau).or.
&
((abs(goal-v)).le.(abs(accel/2/3600*(tau-dt)))))
int=int+dt
endif
a=accel/2*(l-cos(int/tau*3.14159))
(int.eq.(tau*2)) then
sif
int=0
endif
if ((abs(goal-v)/dt*3600).lt.abs(a))
a=(goal-v)/dt*3600
endif
return
end
72
then
then
subroutine readfile(n,dd,d,y,light,limit,Cr,Cd,M,Area,
&
diameter,displacement,nogears,ratio,
&
&
&
torquemax,rpmmax,pertorque,up,dn,idle,
mrpm,mload,velprof,time2,duration2,v2,t,dt,
grid,sfc,eihc,eico,eino)
C*This
reads the files containing the road profile and car data
C*data against distance
C*n=number of data points
to be read from distance data
real d(5000),y(5000),light(5000),limit(5000),dd
integer n
C*car data and incrementer
real ratio(5),Cr,Cd,M,Area,diameter,displacement,transaxle
integer i,nogears
real idle,torquemax,rpmmax,pertorque(12),up(12),dn(12)
C*variables for emissions
C*sfc is in g/kWhr
C*ei.. is as a percentage (gEmmis/gFuel *100)
C*grid determines size of the map. Will be a matrix of grid x grid
real mrpm(10),mload(10),sfc(10,10),
&
eihc(10,10),eico(10,10),eino(10,10)
,integer
grid
C*VELOCITY PROFILE VALUES
C*velprof=y if following a velocity profile
C*time2, duration2, v2: these arrays have a '2' to
C*differentiate them from the values for the route profile.
C*time2init=the initial time
C*t=the number of time data points
character (1) velprof
real time2(5000),duration2(5000),v2(5000),dt,time2init
integer t
C*****
***************************************************
C*reads road (or velocity) profile
if (velprof.eq.'y') then
read (1,*) t,dt
read
(1,*) time2init,duration2(l),v2(l)
time2(1)=0
i=2
do while
(i.le.t)
read (1,*) time2(i),duration2(i),v2(i)
time2(i)=time2(i)-time2init
i=i+l
enddo
else
i=1
read (1,*) n, dd
do while (i.le.n)
read(l,*) d(i),y(i),light(i),limit(i)
i=i+l
enddo
endif
C*reads physical car data
read (2,*) Cr,Cd,M,Area,diameter,displacement
73
read (2,*) torquemax,idle,rpmmax
read (2,*) nogears,transaxle
i=1
do while (i.le.nogears)
read(2,*) ratio(i)
ratio(i)=transaxle*ratio(i)
i=i+l
enddo
C*reads shifting schedule for car
read(3,*) pertorque(l),pertorque(2),pertorque(3),
&
pertorque(4),pertorque(5),pertorque(6)
&
pertorque(7),pertorque(8),pertorque(9)
&
pertorque(1O),pertorque(ll),pertorque( 12)
read(3,*) up(l),up(2),up(3),up(4),up(5),up(6),
&
up(7),up(8),up( 9 ),up(10),up(ll),up(12)
read(3,*) dn(l),dn(2),dn(3),dn(4),dn(5),dn(6),
&
dn(7),dn(8),dn(9),dn(10),dn(ll),dn(12)
C*reads emission maps [emiss(speed,load)]
read(4,*) grid
read(4,*) mrpm(l),mrpm(2),mrpm(3),mrpm(4),mrpm(5),
&
mrpm(6),mrpm(7),mrpm(8),mrpm(9),mrpm(1o)
read(4,*) mload(l),mload(2),mload(3),mload(4),mload(5),
&
mload(6),mload(7),mload(8),mload(9),mload(1O)
i=1
do while (i.le.10)
mrpm(i)=mrpm(i)/rpmmax
mload(i)=mload(i)/torquemax
i=i+1
enddo
i=1
do while
read(4,*)
&
&
i=i+l
enddo
i=1
do while
read(4,*)
&
&
i=i+l
enddo
i=1
do while
read(4,*)
&
&
i=i+l
enddo
i=1
do while
read(4,*)
&
&
(i.le.grid)
sfc(1,i),sfc(2,i),sfc(3,i),sfc(4,i),
sfc(5,i),sfc(6,i),sfc(7,1),sfc(8,i),
sfc(9,i) ,sfc(10,i)
(i.le.grid)
eihc(l,i),eihc(2,i),eihc(3,i),eihc(4,i),
eihc(5,i),eihc(6,i),eihc(7,i),eihc(8,i),
eihc(9,i),eihc(10,i)
(i.le.grid)
eico(l,i),eico(2,i),eico(3,i),eico(4,i),
eico(5,i),eico(6,i),eico(7,i),eico(8,i),
eico(9,i),eico(10,i)
(i.le.grid)
eino(l,i),eino(2,i),eino(3,i),eino(4,i),
eino(5,i),eino(6,i),eino(7,i),eino(8,i),
eino(9,i),eino(10,i)
74
enddo
close (1)
close (2)
close (3)
close (4)
return
end
75
subroutine requestgear(torque,rpm,v,torquemax,rpmmaxpertorque,
&
up,dn,gear,status,nogears)
C*This selects
the gear based on the torque/rpm shift curves
real torque,rpm,v
C*shifting data
C*newup,newdn=rpm where shift is requested - interpolated by torque
real torquemax,rpmmax,pertorque(12),up(12),dn(12),newup,newdn
integer status,nogears,k,gear
k=2
do while (((torque/torquemax).gt.pertorque(k)).and. (k. lt.
k=k+l
enddo
if (k.ne.12) then
call interpolate(pertorque(k-1),pertorque(k),
&
up(k-1),up(k),torque/torquemax,newup)
call interpolate(pertorque(k-1),pertorque(k),
&
dn(k-1),dn(k),torque/torquemax,newdn)
else
newup=up(k)
newdn=dn(k)
endif
12))
((status.le.-l).and.((rpm/rpmmax).le.newdn).and.
&
(gear.gt.1)) then
gear=gear-1
sif
endif
if
if
(status.ge.0) then
(((rpm/rpmmax).lt.newdn).and.(gear.gt.1)) then
gear=gear-1
else if (((rpm/rpmmax).gt.newup).and.(gear.lt.nogears))
gear=gear+l
endif
endif
if
(v.eq.0) then
gear=1
endif
return
end
76
then
subroutine writefile(time,duration,x,v,a,angle,Pb,gear,rpm,
&
bmep,torque,hc,cummhc,co,cummco,no,cummno,light,height,
&
fuel,cummfuel)
C*This writes the time increment calculations
into a
file
integer gear
real
&
&
time,duration,a,v,x,Pb,rpm,bmep,torque,
hc,cummhc,co,cummco,no,cummno,
light,angle,height,fuel,cummfuel
C*** ***********************************************************
write
&
&
&
&
100
format
&
(8,100) time,duration,a,v,x,
height,angle,gear,rpm,Pb,
torque, hc, cummhc, co, cummco,
no,cummno,fuel,cummfuel,light
(f7.2,x,f5.2,x,f7.0,x,f5.2,x,f7.4,x,
f6.0,x,f5.1,x,il
,x,f5.0,x,f7.0,x,
&
f6.1,x,f6.3,x,f6.2,x,f6.3,x,f6.2,x,
&
f6.3,x,f6.2,x,f6.3,x,f6.1,x,f2.0)
return
end
77
References
1.
Cheng, W.K., Hamrin, D., Heywood, J.B., Hochgreb, S., Min, K., and Norris, M.,
"An Overview of Hydrocarbon Emissions Mechanisms in Spark-Ignition Engines,"
SAE paper 932708, SAE International Congress & Exposition, Detroit, MI
2.
Butler, J.W., Jesion, G., St. Denis, M.J., Cicero-Fernandez, P., and Winer, A.M.,
"Effects of In-Use Driving Conditions and Vehicle/Engine Operating Parameters on
'Off-Cycle' Events: Comparison with Federal Test Procedure Conditions," Air &
Waste Management Association, Vol. 44, pp. 31-8, Jan. 1994
78